What you’re describing is called a rabbeted half-blind dovetail. The process is to cut a rabbet on the side of each drawer front that’s 1/2” wide and slightly deeper than the depth of your dovetail. After that, the process is the same as any other half-blind dovetail but made slightly more challenging because you can’t get the saw to much of an angle.

Using a jig like the Leigh, it’s a piece of cake. I’ve done them several times.

Here’s my suggestion. It’s just a piece of shop furniture, not a museum piece. Do a false front. In other words, build your drawer box out of the 1/2” plywood to the correct dimensions to allow for your slides, then screw your 3/4” birch plywood, cut full width, to it.

I think they’re also called French dovetails. I’ve done them, not overly difficult on my Incra router table. Probably the trickiest part is setting up stops to cut the drawer fronts. The drawer sides are cut the entire width top to bottom.